Hi,
In Mathematica version 6.0, I'm having difficulty trying to coax the
input
In[1]:= FullSimplify[{\[ImaginaryI] Abs[a], -\[ImaginaryI] Abs[a]},
Element[a, Reals]]
to produce the set {-\[ImaginaryI] a, \[ImaginaryI] a}.
Interestingly, this *does* result for
In[2]:= FullSimplify[{\[ImaginaryI] Abs[a], -\[ImaginaryI] Abs[a]}, a
>= 0]
and
In[3]:= FullSimplify[{Sqrt[-1] Abs[a], -Sqrt[-1] Abs[a]}, a < 0]
Am I missing something here? I've tried Allan Hayes' suggestion in
2003, with
In[4]:= FullSimplify[{\[ImaginaryI] Abs[a], -\[ImaginaryI] Abs[a]},
Element[a,Reals],ComplexityFunction -> ((Count[#, _Abs, Infinity]) &)]
Out[4]= {\[ImaginaryI] Sqrt[a^2], -\[ImaginaryI] Sqrt[a^2]}
to no avail; of course, I could just add a PowerExand@ to the above
expression, but this seems like a lot to do, especially when
Mathematica already has been explicitly told that "a" is a real
number.
Any tricks or hints would be greatly appreciated!
Regards,
Michael